I looked and saw this on EWTN.com's "Catholic Q&A." The Eastern Catholicism expert, Anthony Dragani, answered it:
Question from on 01-31-2004:
What were the West's objections to Hesychast prayer and what role, if any, can they play in a Latin Catholic's prayer life today?
Answer by Anthony Dragani on 02-20-2004:
There were two primary objections:
1. There was a concern that it reduced mysticism to a specific "method" or "technique." In other words, there was a fear that Hesychast prayer was an attempt to develop some sort of "formula" for spiritual growth, which would neglect the truth that spirituality is about a relationship with God.
2. There was a disagreement with the theology associated with it. Hesychast prayer is very much linked to the theology of St. Gregory Palamas, who taught that God is both essence and energies. The essence of God is that which we can never know, so we experience God through his uncreated energies. Grace is another name for these energies. Thus, Hesychasm advocates the position that when we experience grace, we are experiencing God Himself. This view of grace was very different from the view advocated in much of Scholastic Theology in the West.
Today these concerns are no longer held, and the Western Church recognizes the validity and full legitimacy of Hesychast prayer. Pope John Paul II even asked Byzantine Catholic Churches to restore St. Gregory Palamas to their calendars, as many had previously removed him.
Can Hesychast prayer play a role in the life of a Latin Catholic? Absolutely! Many Roman Catholics have read the wonderful book "The Way of a Pilgrim," and now routinely say the Jesus Prayer.
God Bless, Anthony
The EC's venerate St. Gregory Palamas.
Hesychasm is just an Eastern tradition. In the West, we have many mystical traditions of our own. (I'm going to read St. John of the Cross's Ascent of Mount Carmel soon.) I don't subscribe to the distinction between essences and energies. God is God. To each his own!